Given that the present value of a basic annuity-due with n payments is 12 and gi

Question

Given that the present value of a basic annuity-due with n payments is 12 and given that the present value of a basic annuity-due with 2n payments is 21, find the present value of a basic annuity-immediate with 4n payments.

Explanation / Answer

PV_Annuity due = C*(1+i)*(1/i)*(1-(1+i)^-n) Given present value of a basic annuity-due with n payments is 12 =>C*(1+i)*(1/i)*(1-(1+i)^-n) = 12 and present value of a basic annuity-due with 2n payments is 21 =>C*(1+i)*(1/i)*(1-(1+i)^-2n) = 21 If n = 1 =>C*(1+i)*(1/i)*(1-(1+i)^-n) = 12 =>C = 12 and C*(1+i)*(1/i)*(1-(1+i)^-2n) = 21 =>12*(1/i)*(1/1+i)*(i^2+2i) = 21 =>12*(i+2/i+1) = 21 =>12i+24 = 21i+21 =>9i = 3 =>i = 1/3 So present value of a basic annuity-immediate with 4n = 4 payments is C*(1+i)*(1/i)*(1-(1+i)^-4) = 12*(4/3)*(3)*(1-((4/3)^(-4))) = 32.8125

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